Dear Joe, thank you for the very interesting topic and initiated discussion. It seems the discussion is probably going to take further waves in the near future, since power meters are getting more affordable and more people will meet these issues, especially if powermeters become more compatible with more bikes. In my example I race with a XC bike but train on a roadbike as well and on a trainer with my spare bike in bad weather.
I would first like to react to the very first comment and then add my own case and experiences, conclusions for thoughts, due to the significant difference of 20 BPM I noticed myself outdoor vs indoor during two efforts with equal wattage.
The very first comment from Marcus on a possible explanation of the roller-resistance indoors vs the "free roll-out" outdoors initially seemed like a plausible aspect, but at further thought there is always a resistance that creates wattage: either through acceleration, through the effort needed to overcome gravity on a climb, the wind resistance on the flat, rolling resistance of the tires/bearings, etc. or the resistance of the indoor trainer (magnet). So even when you ride on the flat, the wind's resistance at a speed where you create such force to keep up your maximum effort for the 20min (which should mean a lot of wind et al resistance) should be a constant force. In other words, there is no "free roll-out" where you would suddenly be in a vacuum with chance for recovery or decreased wattage. If you let off on the torque, it simply means a drop in your wattage, meaning no sustained effort, but these inbetweens could be traced easily afterwards by looking at your effort level graphically and any drops in that. Equally, you can let off on a climb or on an indoor trainer as well.
The fact that the trainer's magnet slows down the effort, is irrelevant when you choose not to exert the effort while it slows down: the test is not about constant speed, but about exerted effort. In addition, if due to some slowing down (esp on hillclimbs or on trainers) the resistance suddenly decreases and you want to get back on the same cadence and/or speed, it simply means that you are initially on a lower wattage, which you need to compensate immediately through a higher wattage than before, to get back on track. This change in effort however will be equal in the case of hillclimb, trainer or flat (with wind + other resistance), as the counter forces are constant.
One very small impact I would add to this, which is of course much less relevant in case of air: in water, water displacement means that keeping a momentum requires less effort on short distances than slowing down and suddenly getting back on the same speed, just try accelerating with a boat from standstill vs in movement. In other words, water "carries us" along for a little while. But in case of air, this is neglectible in compariosn to our body weight, especially considering the very small differences of letting off on the wattage for micro-recovery split-seconds.
As for my personal experience: incidentally I am about the same age as the subject at the time of writing and have started biking about the same time ago, so feel the relevance of getting to know my limits and developing myself in a proper manner. Since I am new to power meters (got one to try out for some weeks), I stumbled on this same issue and found your article, which is quite useful for understanding the differences and prepare myself for races. I am trying to find answers the same way for my case from the past 2 days.
I haven't done a full FTP yet, but had an indoor session on a roller with two 240W efforts of 10min with 5min recovery inbetween. I could not manage to perform the second one fully, true enough though it was preceded by some efforts for 40min, of which around 200W for 20min. Next day however I was using the same bike outside on a hill climb of 9% and found that doing 240W was easy as pie after a 15min warm-up. True enough, I only did one ride of ca 9min on that hill and no second one, but this one was in no comparison with the previous day's first 240W exertion, when even the first 10min was on the edge with serious strain.
The relevant part I consider to be the heartrate comparison of the two occasions: while on day1 I peaked around 181BPM for the first 10min (for accurate comparison 180BPM after 9min, while reaching 170BPM after 2min into the effort), on day2 on the hill climb outside my HR reached only 163BPM, up from 157BPM from the first minutes of the climb. This I consider to be a huge difference in HR for about the same effort exerted and according to my morning HRV measurement I was equally rested on both days, in fact on the first day I had a restday before.
As my individual anaerobic threshold is around 220W @ 167-168 BPM currently, these two divergent results make a tremendous difference in my self-evaluation. Of course there is a major distortion probably due to the earlier mentioned 40min prior efforts, still the perceived effort difference was tremendous.
Since I am a XCM mountainbiker and the powermeter supports me temporarily in my roadbike training sessions, I am unlikely to find a good objective measure of my abilities this way, as I would need to use a consistent measurement, which seems to diverge on roadbike inside, outside and most likely MTB outside as well.
From the comments on your writing I have gathered some useful insights, but do not see a single most important determinent of the differences. I would think it's probably a combination of many factors:
1. mostly the cooling aspect, though some riders are using fans or are outdoor and see no substantial difference;
2. perhaps the oxygen uptake, though I have understood that we never make full use of the oxygen from the air we breathe in, so for such a short test and my particular example at lower effort, this should not be a major determinent;
3. probably the physical movement on the bike which can follow your specific neuro-muscular pathways better than a steady trainer. I am inclined to see this as a major factor;
4. most likely the mental state of being outside and a more focussed mind: I noticed during earlier indoor tests of step-wise raising of the wattage by 30W every 3min that when they take blood to measure the lactate changes at each step, while I'm holding my head still (as blood is taken from my earlobe) during these few seconds my HR actually DEcreases slightly after this concentrated effort, even when my wattage remains stable.

The following is a question from a coach. He and the athlete he coaches are somewhat frustrated by the difference inpower numbers they produce relative to heart rate when riding indoors as opposed to out on the road. This is a common complaint this time of year, one that I hear a lot. ----------...